Representatives for the United Kingdom (U.K.) and the European Union (EU) kicked off Brexit negotiations in Brussels on June 19, nearly 12 weeks after Britain's prime minister triggered the mechanism that would let it depart from the EU.
Michel Barnier, the European Union chief negotiator, and David Davis, the Brexit minister, stressed after their talks that an exit deal was achievable, but both conceded they were up against the clock, with Britain set to leave in March 2019.
While Mr Barnier insists on the "sequencing" of talks, so that trade negotiations can not start until probably January, finding a way to avoid a "hard" customs border for troubled Northern Ireland may well involve some earlier discussion of the matter. "We will work all the time with the UK, and never against the UK", Barnier said.
"Then in the second step, we scope our future partnership; we also agree on how we structure our tools".
European Union officials had earlier warned May not to make that offer so early in the talks.
"In the first step, the negotiation rounds will be broken down into three groups: citizen rights, the single financial settlement, and other separation issues", Barnier said.
But Mr Barnier added that he was "not in a frame of mind to make concessions", and suggested the United Kingdom would have to face up to "substantial" consequences of leaving the EU.
But May's mandate for a hard Brexit has since eroded after her Conservative party lost its parliamentary majority in the June 8 general election.
At Monday's press conference Davis said trade would be discussed alongside the divorce issues, citing the EU's own withdrawal clause.
He said there was a "very sensitive political context" given the looming deadline for forming a Northern Ireland Executive, the fact that a new Government is only recently in place in Dublin and the "ongoing political discussions" in London.
While the United Kingdom has said repeatedly that it wants out of the EU's single market and customs union - which offers tariff-free access to the EU, but requires countries to cede power to make their own trade deals - the DUP's manifesto says it wants a customs agreement and "arrangements to facilitate ease of movement of people, goods and services". "We must secure a deal that works for all parts of the United Kingdom, and enables us to become a truly global Britain".
"There is a long way to go, but we are off to a promising start.
David Davis and I, as chief European Union negotiator, will discuss the issues together, tackle difficulties, and lift obstacles", he added. The last round, according to the current schedule, will start on 9 October, 10 days before the European Union summit where leaders are expected to assess the progress made. "The UK has made a decision to leave the EU".
"We must first tackle the uncertainties caused by Brexit", Barnier said, citing the rights of European Union citizens in Britain and the possible impact on the open border between Northern Ireland and Ireland.
"The best way we can spend this week is to rebuild trust", rather than tackle the big hard issues right at the start, a European source said.
They first exchanged gifts - a mountain walking stick from Barnier's Savoy region in the French Alps for Davis, a book on Annapurna climbing for Barnier.
"Because membership of the single market requires the four freedoms [of people, goods, services and capital] to be abided, and [because] we need to bring back to Britain control of our laws, control of our borders, we'll be leaving the single market", he said. "Every one must assume the consequences, they are massive", he said.
Quoting Winston Churchill, Davis said in response: "A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty".